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The Cauchy Residue Theorem With Applications

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The Cauchy Residue Theorem With Applications

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Author : Augustin Cauchy
language : en
Publisher:
Release Date : 2019-09-28

The Cauchy Residue Theorem With Applications written by Augustin Cauchy and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-28 with categories.

This is a translation of "Mémoir sur les Intégrales Définies, prises entre des Limites Imaginaires." by Augustin Louis Cauchy, available from www.e-rara.ch. You will need to be well versed in Integral Calculus and the theory of complex variables to be able to understand this memoir. It will also help if you are already familiar with the Residue Theorem. This memoir contains a plentiful number of applications of the Residue Theorem to real definite integrals.

The Cauchy Method Of Residues

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Author : Dragoslav S. Mitrinovic
language : en
Publisher: Springer Science & Business Media
Release Date : 1984-04-30

The Cauchy Method Of Residues written by Dragoslav S. Mitrinovic and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984-04-30 with Mathematics categories.

Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not' grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory arid the struc ture of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "completely integrable systems", "chaos, synergetics and large-5cale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics. This program, Mathematics and Its Applications, is devoted to such (new) interrelations as exampla gratia: - a central concept which plays an important role in several different mathe matical and/or scientific specialized areas; - new applications of the results and ideas from one area of scientific en deavor into another; - influences which the results, problems and concepts of one field of enquiry have and have had on the development of another.

The Cauchy Method Of Residues

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Author : Dragoslav S. Mitrinovic
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01

Volume 1, i. e. the monograph The Cauchy Method of Residues - Theory and Applications published by D. Reidel Publishing Company in 1984 is the only book that covers all known applications of the calculus of residues. They range from the theory of equations, theory of numbers, matrix analysis, evaluation of real definite integrals, summation of finite and infinite series, expansions of functions into infinite series and products, ordinary and partial differential equations, mathematical and theoretical physics, to the calculus of finite differences and difference equations. The appearance of Volume 1 was acknowledged by the mathematical community. Favourable reviews and many private communications encouraged the authors to continue their work, the result being the present book, Volume 2, a sequel to Volume 1. We mention that Volume 1 is a revised, extended and updated translation of the book Cauchyjev raeun ostataka sa primenama published in Serbian by Nau~na knjiga, Belgrade in 1978, whereas the greater part of Volume 2 is based upon the second Serbian edition of the mentioned book from 1991. Chapter 1 is introductory while Chapters 2 - 6 are supplements to the corresponding chapters of Volume 1. They mainly contain results missed during the preparation of Volume 1 and also some new results published after 1982. Besides, certain topics which were only briefly mentioned in Volume 1 are treated here in more detail.

Fundamentals And Applications Of Complex Analysis

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Author : Harold Cohen
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-07-31

Fundamentals And Applications Of Complex Analysis written by Harold Cohen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-07-31 with Mathematics categories.

This book is intended to serve as a text for first and second year courses in single variable complex analysis. The material that is appropriate for more advanced study is developed from elementary material. The concepts are illustrated with large numbers of examples, many of which involve problems students encounter in other courses. For example, students who have taken an introductory physics course will have encountered analysis of simple AC circuits. This text revisits such analysis using complex numbers. Cauchy's residue theorem is used to evaluate many types of definite integrals that students are introduced to in the beginning calculus sequence. Methods of conformal mapping are used to solve problems in electrostatics. The book contains material that is not considered in other popular complex analysis texts.

Complex Analysis With Applications In Science And Engineering

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Author : Harold Cohen
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-04-23

Complex Analysis With Applications In Science And Engineering written by Harold Cohen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-04-23 with Mathematics categories.

The Second Edition of this acclaimed text helps you apply theory to real-world applications in mathematics, physics, and engineering. It easily guides you through complex analysis with its excellent coverage of topics such as series, residues, and the evaluation of integrals; multi-valued functions; conformal mapping; dispersion relations; and analytic continuation. Worked examples plus a large number of assigned problems help you understand how to apply complex concepts and build your own skills by putting them into practice. This edition features many new problems, revised sections, and an entirely new chapter on analytic continuation.

Introductory Complex And Analysis Applications

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Author : William R. Derrick
language : en
Publisher: Academic Press
Release Date : 2014-05-10

Introductory Complex And Analysis Applications written by William R. Derrick and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.

Introductory Complex and Analysis Applications provides an introduction to the functions of a complex variable, emphasizing applications. This book covers a variety of topics, including integral transforms, asymptotic expansions, harmonic functions, Fourier transformation, and infinite series. Organized into eight chapters, this book begins with an overview of the theory of functions of a complex variable. This text then examines the properties of analytical functions, which are all consequences of the differentiability of the function. Other chapters consider the converse of Taylor's Theorem, namely that convergent power series are analytical functions in their domain of convergence. This book discusses as well the Residue Theorem, which is of fundamental significance in complex analysis and is the core concept in the development of the techniques. The final chapter deals with the method of steepest descent, which is useful in determining the asymptotic behavior of integral representations of analytic functions. This book is a valuable resource for undergraduate students in engineering and mathematics.

Complex Analysis And Applications

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Author : William R. Derrick
language : en
Publisher: Thomson Brooks/Cole
Release Date : 1984

Complex Analysis And Applications written by William R. Derrick and has been published by Thomson Brooks/Cole this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Mathematics categories.

Developments Obtained By Cauchy S Theorem

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Author : Henry Parker Manning
language : en
Publisher:
Release Date : 1891

Developments Obtained By Cauchy S Theorem written by Henry Parker Manning and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1891 with Cauchy problem categories.

Complex Analytic Functions Theory And Applications

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Author : S. K. Sharma
language : en
Publisher: New Age International
Release Date : 2000

Complex Analytic Functions Theory And Applications written by S. K. Sharma and has been published by New Age International this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with categories.

In A Simple And Interesting Style, This Book Explains The Various Concepts In Complex Analysis And Illustrates Them Through Practical Applications. Starting With A Definition Of The Properties Of A Complex Number, The Book Goes On To Explain Complex Variables And Conformal Mapping. It Then Presents An Exhaustive Description Of Schwarz -Christoffel Transformation Which Is Followed By A Discussion Of Complex Integration And Singularities And Residues.The Book Explains Both Simple And Sophisticated Applications. In The Former Category Are Mechanical Vibrating Systems, Electric Circuits Etc., While In The Latter Category Are Problems In The Theory Of Heat, Fluid Mechanics, Electrostatics, Dam Designs Etc.With Its Rich And Lively Discussion Of An Important Mathematical Method, This Book Would Be Extremely Useful For Both Science And Engineering Students. Researchers And Practising Engineers Would Also Find It A Valuable Reference Source.

The Laplace Transform

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Author : Joel L. Schiff
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-05

The Laplace Transform written by Joel L. Schiff and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-05 with Mathematics categories.

The Laplace transform is a wonderful tool for solving ordinary and partial differential equations and has enjoyed much success in this realm. With its success, however, a certain casualness has been bred concerning its application, without much regard for hypotheses and when they are valid. Even proofs of theorems often lack rigor, and dubious mathematical practices are not uncommon in the literature for students. In the present text, I have tried to bring to the subject a certain amount of mathematical correctness and make it accessible to un dergraduates. Th this end, this text addresses a number of issues that are rarely considered. For instance, when we apply the Laplace trans form method to a linear ordinary differential equation with constant coefficients, any(n) + an-lY(n-l) + · · · + aoy = f(t), why is it justified to take the Laplace transform of both sides of the equation (Theorem A. 6)? Or, in many proofs it is required to take the limit inside an integral. This is always fraught with danger, especially with an improper integral, and not always justified. I have given complete details (sometimes in the Appendix) whenever this procedure is required. IX X Preface Furthermore, it is sometimes desirable to take the Laplace trans form of an infinite series term by term. Again it is shown that this cannot always be done, and specific sufficient conditions are established to justify this operation.

The Cauchy Residue Theorem With Applications

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